Daniel Chan (University of New South Wales) Friday 24 June, 12-1pm, Place: Carslaw 375 2-hereditary algebras and almost Fano weighted projective surfaces Tame hereditary algebras are a classical objects of study in the representation theory of finite dimensional algebras. They include path algebras of extended Dynkin quivers as examples. In the 1980’s, Geigle and Lenzing gave an intriguing approach to studying their representation theory by showing that, up to Morita equivalence, they are classified by certain non-commutative analogues of the projective line, namely the Fano weighted projective lines. Furthermore, the nice representation theory of tame hereditary algebras could be deduced from the nice module theory of the corresponding weighted line via tilting theory. In this talk, we will examine a dimension 2 generalisation of this picture as introduced by Iyama and his school in the last decade.